This Letter shows that interleaved sequences of short pulses in the manner of 'Delays Alternating with Nutation for Tailored Excitation' (DANTE) with N = 1,2,3 . . . equidistant pulses per rotor period extending over K rotor periods can be used to excite, invert or refocus a large number of spinning sidebands of spin-1/2 nuclei in paramagnetic samples where hyperfine couplings lead to very broad spectra that extend over more than 1 MHz. The breadth of the response is maintained for rf-field amplitudes as low as 30 kHz since it results from cumulative effects of individual pulses with very short durations.